ES2386449B1 - PROCEDURE AND DEVICE OF DATA COMMUNICATION THROUGH IMPROVED NOISE MEDIA. - Google Patents

Abstract

Refinement of the object of the application P200900343 entitled "Procedure and device for data communication through noisy means", to improve protection against errors in the transmission of information through a channel or means of noisy transmission. The improved procedure and device consists in the use of a new type of parity matrix structure for the technology of low density parity codes (Low Density Parity Check Codes) in the coding and decoding of data, which improves the performance of error correction without increasing the complexity of the hardware implementation.

Description

IMPROVEMENT OF THE SUBJECT OF THE APPLICATION P200900343 WITH TITLE "PROCEDURE AND DEVICE OF COMMUNICATION OF

DATA THROUGH NOISE MEDIA "

FIELD OF THE INVENTION

The present invention applies to the field of data transmission, and more specifically, to the communication of data through noisy means, that is, media or channels that can introduce errors in the communication.

BACKGROUND OF THE INVENTION

In communication environments it is usual for the transmission medium or external signals to introduce errors in the signal. These errors must be detected and, if possible, corrected at reception to retrieve the correct information. There are multiple ways to include error detection and correction in the state of the art, one of them being the encoding and decoding of information based on low density parity codes

(Low-Density

Parity-Check codes) for the correction from

mistakes .

The

codes from parity from low density

(called

LDPC or low-density parity-check code) They are

error correction codes that are used in the transmission of messages over noisy transmission channels. These codes introduce a certain amount of redundancy in the message (a larger number of bits is sent than the original message), but in such a way that it is possible in reception to receive errors in the received message and correct them.

An LDPC code is a code whose parity matrix is not very dense, that is, the vast majority of its elements are zeros. These types of codes were published

for the first time in the early sixties, by Robert G. Gallager "Low Density Parity Check Codes,"

M. l. T. Press, 1963, and proved to have benefits very close to the well-known Shannon limit (theoretical maximum of the data transmission rate). However, with the original definition of the codes and technology of the time, an affordable implementation with adequate complexity was not possible. Recently, thanks to the evolution of integrated circuits and the invention of structured matrices, these codes have once again become of great interest.

In the state of the art there are multiple methods for coding and decoding against errors. Some methods are those published in patents US 7, 343,548B2 and US 7, 203,897B2, both of which are entitled "Method and ilppilriltus for encoding ilnd decoding dutu" which present methods to improve protection against errors in data transmission. The invention can also be related to the IEEE802 standards. 16e and 802. 11n, which have coding and decoding for error reduction.

It is known in the state of the art that having columns with Hamming weight equal to or less than 2 in the parity matrix restricts the performance of the LDPC codes. However, due to complexity of implementation

of the encoder, matrices with a "double diagonal bl" section have been used in the state of the art.

However, the need for a coding method that increases the robustness of the correction of transmission errors without increasing the complexity of the hardware in the implementation of the error protection device continues to exist in the prior art.

The present invention relates to improvements introduced on the object of the application P200900343, which presents a method and system that solves the above problems, but in which there is still a need for additional coding matrices to those presented therein that allow offering alternatives and even optimize said invention.

Throughout this document a specific nomenclature is used to differentiate the elements used throughout the description of the invention. An uppercase and bold letter (for example, A) indicates

that

he element is a matrix; a lyrics lower case Y

bold font

(by example, to ) indicates that he element is a

vector,

While that a lyrics lower case Y without bold font

(example

to) indicates that he element is a value climb .

On the other hand, the scalar elements that make up a

matrix of dimensions M xN are indicated in the form a (i.j)

where the tuple (i.j) is the position of said element within the matrix being 05i5M ~ 1 the row number and 0 5j5N -1 the column number. The elements that make up a vector

ai)

of dimension M are recorded in the form being (i) the position of the element in the vector (O'5.i.'5.M-l).

In addition, the term cyclic rotation is used throughout the invention, which is defined below. A cyclic rotation z on a vector a ~ [a (O), a (I), ..., a (M -2), a (M -1)] consists of rotating cyclically its elements to the right obtaining the vector [a «Mz)% M) • ... • a« Mzl)% M)] as a result, with% being the "module" operator. In the same way, a cyclic rotation z applied on a matrix A = [a (O), ..... a (N -1)] operates on its columns obtaining the matrix

[a ((N -z)% N), ..., a ((N -z -l)% N)] as a result. The cyclic rotation can also be defined in the opposite direction (to the left) so that a cyclic rotation z

toward

the right is equivalent e to a rotation cyclic

M -z

Y N -z respectively for vec tor Y matrix toward the

left .

DESCRIPTION OF THE INVENTION

In order to achieve the objectives and avoid the convenient ones indicated in previous sections, the invention consists of a procedure and device for the communication of data through noisy means. Specifically, the invention features a data coding method used in transmission, its associated coding device, a decoding procedure, and its associated decoding device. This group of inventions form a single inventive concept, which is described below. If the procedure or device is used in transmission, the equivalent must also be used in reception, and vice versa, in order to retrieve the information sent.

The data coding procedure is applied in transmission and generates parity bits over a block of information so that a code word of N bits (N) K) is generated from a K-bit word that includes protection against errors. Said procedure comprises multiple steps. First, a factor b is selected which is a natural number between 1 and K so that the division of N Y K between factor b is natural numbers (n = N / bi k-K / b). Next, a binary model matrix is defined

of size (n-k) x n as the combination of a submatrix corresponding to the positions of the information bits Ha Y of a submatrix corresponding to the

bits of parity Hb l where said second submatrix is composed of a column vector of n-k

hbO positions And a matrix "bl with triple diagonal structure, that is, where the elements of the two central diagonals (i, i), (i + J, i), 05.is.n-k-2 and of the

hb1 hb1

diagonal of the last line hbJn-k-l, O) are equal to 1, where n-k is the number of rows and columns of the matrix

"b

I

And the rest of the elements are equal to zero. Then, the compact matrix "1y is generated and from it the parity matrix H From there a block of

information and the parity matrix H on the information block is used to determine the parity bits corresponding to said block. Finally, the parity bits are transmitted together with the information block. In an implementation of the procedure it is possible to eliminate one or more elements of the code word before being transmitted, reducing transmission redundancy without seriously worsening the ability to protect against errors. This technique is called "puncturing technique." In this case the transmitted word will have a smaller number of bits than the code word obtained with the initial procedure. The data coding device comprises means for storing the compact matrix HI derived from

a binary model matrix "o :::: [Ha I" b] formed as the combination of a submatrix corresponding to the positions of the information bits Ha Y of a submatrix corresponding to the parity bits "b 'where

said second submatrix Hb ~ [hb <lIHbll is composed of a

vector column of n-k positions and a structure "bl

hbO

triple diagonal, that is, where the elements of the two central diagonals hbI U, i), hbl (i + l, i), 05, iS.n-k-2 and of the

diagonal of the last line hb¡ {n -k-l, O) are equal to 1, being n-k the number of rows and columns of the matrix "b 'And the rest of the elements are equal to zero¡ and of a

The microprocessor that takes the information block, uses the compact matrix "1 to generate the parity matrix H, applies the parity matrix H to the information block to obtain the parity bits corresponding to said

block and add the parity bits to the information block before being transmitted.

In a specific implementation of this device, one or more elements of the code word are removed after adding the parity bits to the information block but before transmitting, applying the puncture technique. In this way the transmitted word will have a smaller number of bits than the originally generated code word.

On the other hand, the data decoding procedure operates on reception and estimates the block of information received from a signal vector received from the channel. From a code word received from N bits (which may have errors due to channel noise), the K bit information word that the transmitter wanted to send is obtained. This procedure initially takes a signal vector from the channel and matrix

binary model that is a combination of a submatrix corresponding to the positions of the information bits Ha Y of a submatrix corresponding to the parity bits where said second submatrix is composed of a column vector of n-k

hbO positions and a H bl tripl and diagonal structure, this

is I

where the elements from the two diagonals central

h "(i, i),

h "(i + l, i), 05: i $ n -k -2 Y from the diagonal from the last

line

hb¡ {n-k -l, O) They are equals to one, being n-k he number from

rows and columns of the matrix "b 'And the rest of the elements are equal to zero. Then it generates the compact matrix" 1 and from it the matrix of parity H, and finally estimates the block of information from the received signal vector and of the parity matrix H. If the puncture technique was used in transmission, it is necessary to recover the information lost at reception. In this case, an indicator value is inserted in the positions eliminated by the transmission punch technique, before estimating the information block from the received signal vector and the parity matrix. The data decoding device comprises means for storing the compact matrix "1

derived from a binary model matrix ", = [". 1 ",] formed as the combination of a submatrix corresponding to the positions of the information bits" and a submatrix corresponding to the parity bits "b 'where said second submatrix H b = [hbQ IH b1] is composed of a column vector of nk positions h bO and a structure "triple diagonal bl, that is, where the elements of the two central agonal di h (i, i), h (i + l, i), O ~ i ~ nk -2 Y of the

b1 b1

diagonal of the last line hb¡ {nkI, O) are equal to 1, where nk is the number of rows and columns of the matrix "b" and the rest of the elements are equal to zero; a microprocessor that generates the matrix of parity H from the compact matrix "1" applies said parity matrix H on the received signal vector, and estimates the block of

•

ES 2 386449 Al

information received If the transmitting device used the puncture technique, it is necessary to recover the lost information before performing the error correction. Therefore, S in this implementation and before applying the parity matrix H on the received signal vector, an indicator value is inserted in the positions eliminated by the transmission puncture technique. In one implementation it is possible to use one of 10 the following compact matrices "1to obtain 336-bit code words with an encoding rate of ~. The matrix:

13 -1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 or -} -1 -1 -1 -} -1 -1 -1 -1 -1 S -1 -1 -1 11 -1 -1 -1 4-1 6 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 -1 15 -1 13 -1 -1 -1 -1 II -1 10 -1 9 13 -} -1 oo -} -1 -} -1 -} -1 -} -} -1 -1 13 -1 -1 6 -1 10 -1 5 -1 -1. 4 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -} -1 2 11 -} -1 -} -1 -} -1 -1 -1 -1 -1 oo -1 - 1 -1 -1 -1 -1

o o

, -, -one

-1 -1 9 -1 -1 -1 -1 -1. -1 -1 -1 -1 -1 -1 or o -1 -1 -1

20 2 -1 13 -1 9 -1 -1 -1 -1 -1 -1. -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 11 -1 -1 -1 -1 -1 -1 4 11 12 -1 -1 -1 -1 -1 - 1 -1 -1 oo -1 -1 -1 -1 -1 10 -1 -1 -1 -1 1 -1 13 13 -1 -1 -1 -1 -1 -1 -1 -1 -1 OO - 1 -1 -1 O -1 -1 O 2 2 -1 -1 -1 -1. O -1 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 -1 -1 -1 -1 -1 -1 2 11 2 4 12 -1 -1 -1 -1 - 1 -1 -1 -1 -1 or

or the matrix:

-1 -1 -1 6 -1 -1 9 6 -1 -1 2 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 O -1 -1 -1 3 -1 12 1 -1 -1 3 -1 O or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 9 11 -1 -1 13 -1 -1 2 12 - 1 -1 -1 -1 OO -1 -1 -1 -1 -1 -1 -1 -1 30 1 -1 -1 11 -1 -1, -1 -1 -1 11 -1 -1 -1 - 1 OO -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 4 a -1 -1 -1 -1 -1 2 S 4 -1 -1 -1 OO -1 -1 -1 -1 -1 -1 -1 3 O -1 -1 a -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 O or -1 -1 -1 -1 -1

-1 -} -1 O 6 -} -1 -} -1 5 13 -} -1 -1 -} -1 -1 -1 oo -1 -} -1 -1 -1 -} -1 9 -1 -} -1 3 -1 -} -1 -1 -1 -1 -1 -1 -1 OO -1 -1 -1

35 9 O 13 -1 -1 12 -1 -1 8 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 O O -1 -1

-

1 5 -1 -} 4 -1 -} 5 -} -1 -} -1 -1 -1 -1 -1 -1 -1 -1 -1 or o -1

-1 -1 -1 8 -1 -1 8 -1 -1 9 O -1 O -1 -1 -1 -1 -1 -1 -1 -1 -1 O O

10 11 -1 -1 -1 3 -1 -1 O -1 -1 -1 8 -1 -1 -1 -1 -1 -} -1 -1 -1 O

40 In another implementation it is possible to use one of the following compact matrices "1to obtain 1920 bit code words with a coding rate of 1/2. The matrix:

-

1 52 -1 64 -1 -1 60 -1 -1 -1 -1 1. -1 O -1 -1 -1 -1 -1 -1 -1 -1 -1 -1

ES 2 386449 Al

10 -1 -1 -1 -1 79 -1 -1 19 -1 18 51. -1 OO -1 -1 -1 -1 -1 -1 -1 -1 -1 9 -1 -1 -1 -1 -1 -1 7S 29 72 -1 -1 -1 OO -1 -1 -1 -1 -1 -1 -1 -1 -1 52 16 63 -1 -1 65 -1 -1 -1 -1 -1 . 40 -1 -1 or o -1 -1 -1 -1 -1 -1 -1 -1 24 -1 -1 39 -1 -1 -1 -1 -1. -1 -1 -1 -1 O O -1 -1 -1 -1 -1 -1

"1 -1 -1 -1 -1 -1 -1 -1 53 79 48 -1. -1 -1 -1 -1 -1 O or -1 -1 -1 -1 -1

-

1 O -1 -1 -1 61 51 -1 -1 -1 -1. -1 -1 -1 -1 -1 -1 OO -1 -1 -1 -1 -1 -1 -1 -1 SO -1 -1 -1 -1 15 -1 -1 -1 -1 -1 - 1 -1 OO -1 -1 -1

"

15 -1 19 -1 -1 -1 -1 -1 7S YES 43 -1. -1 -1 -1 -1 -1 -1 -1 -1 O O -1 -1 12 -1 -1 -1 38 -1 -1 -1 69 -1 62 -1. -1 -1 -1 -1 -1 -1 -1 -1 -1 O O -1 -1 19 -1 41 -1 -1 41 -1 -1 -1 -1. O -1 -1 -1 -1 -1 -1 -1 -1 -1 OO 41 -1 11 -1 -1 -1 -1 -1 15 -1 30 -1 40 -1 -1 -1 -1 - 1 -1 -1 -1 -1 O

Or the matrix:

27 -1 -1 -1 55 19 -1 ~ -1 -1 -1 -1 -1 or -1 -1 -1 -1 -1 -] -1 -1 -1 -1 -1 -1 or -1 1 -1 70 -1 47 -1 62 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 41 -1 -1 -1 44 -1 -1 59 W 25 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 16 77 -1 -1 -1 -1 48 -1 -1 -1 -1 -1 -1 -1 oo - 1 -1 -1 -1 -1 -1 -1

-

} -} -} 45 -} 27 -} 46} 9 -1 -} -1 -1 -} -1 -1 oo -1 -1 -1 -} -1 -} -} -1 63 -1 -} -} 55 -1 -} -1 48 26} O -} -1 -1 -1 oo -1 -1 -} -1 -} -1 -1 -1 42 -1 21 -1 58 -1 41 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 79 or -1 7 S2 -1 -1 -1 -1 -1 -1 - 1 -1 -1 -1 oo -1 -1 -1 -1 29 -1 -1 -1 37 -1 -1 -1 35 21 -1 -1 -1 -1 -1 -1 -1 -1 oo - 1 -1 -1 -1 22 72 -1 -1 47 -1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 35 -1 -1 - 1 -1 13 -1 35 -1 70 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 46 28 -1 -1 -1 38 -1 -1 - 1 -1 10 59 -1 -1 -1 -1 -1 -1 -1 -1 -1 W

In another implementation it is possible to use one of

the following compact matrices "1 to get words

8640 bit code with an encoding rate of 1/2. The

matrix:

~ "'~" ~ I "_ ~ O ~~~~~~~~~~

290 O 312 -1 32 -1 120 -1 -} -1 -} -1 -} oo -1 -} -1 -} -1 -} -1 -} -} 183 57 -} -} 187 68 -} -} -} -} 260 -1 8} -} oo -} -} -} -1 -} -} -} -} -1 -1 -1 323 -1 -1 -1 137 3S4 -1 -1 162 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -} -1 228 -1 -} -} -} 224 -} 114 -} 245 -} -1 -} -1 oo -} -one -} -} -} -}

113 98 120 23 O O 1 -} -1 -} -1 -} -} -} 138 -} 187 45 62 -} -1 -1 -1 -} -1 or o -} -} -} -}

-1 -1 142 -1 -1 -} 347 67 -1 -} -1 46 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 -1 n9 265 -1 66 156 96 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 212 184 -} -}} 02 -} -} -} -}} 20 - } -1 -} -1 -} -1 -} -} -} -1 -} oo -}

-1 -1 -1 -1 -1 -1 -1 90 15 -1 329 153 or -1 -1 -1 -1 -1 -1 -} -1 -1 oo 207 70 -} 7 235 -} -} -1 -1 -} -} -1 8}} 85 -} -1 -} -1 -} -1 -} -1 -} or

or the matrix:

-

1 34 -1 95 -1 279 -1 -1 -1 -1 249 -1 -1 O -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -} -} O-} O -} -} -} -} 134 356 275 -} O or -1 -} -} -1 -1 -1 -} -} -} 51 -1 27 -1 -1 -1 -1 -1 22 152 - 1 57 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 -1} 24 -1 290 -1 281 15 -} -1 -} -1 -1 -} -1 -} oo -1 -} -1 -} -} -} -1 -1 340 -1 99 336 -} -1 -1 -1 -1 -1 33 -1 -1 -1 oo -} -1 -} -1 -1 -1 163 -} 46 -} -1 -} -1 -} -1 306 -1 86 -} -1 -} -1 -1 oo -1 -} -} -1 -} -1 lBS -1 24 -1 -1 -1 94 or -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 223 -1 225 325 -} -1 -1 - 1 -} 297 -1 -} -1 -1 -1 -} -1 -1 oo -} -} -} 46 -1 314 -} -1 -} 59 -} -1 67 -1 120 -} -1 -} -1 -} -1 -} -1 oo -1 -} -} -1} 21 -1 -1 -1 -1 161 -1 303 -1 264 -1 -1 -} -1 -} -1 -} -1 -} oo -} -1 303 -1 -1 185 -1 -} 138 -} -1 -1 or -1 -} -1 -1 -} -} -1 -} -} oo

ES 2 386449 Al

-1 -1 312 -1 -1 -1 100 -1 -1 144 -1 307 33 166 -1 -1 -1 -1 -1 -1 -1 -1 -1 W

In another implementation it is possible to use the following compact matrix to obtain code words

H1

1440 bits with an encoding rate of 2/3

49 -1 -1 21 31 -1 57 -1 -1 19 -1 29 2 -1 19 -1 -1 or -1 -1 -1 -1 -1 -1 -1 7 22 -1 -1 37 -1 32 10 -1 26 -1. -1 59 -1 48 -1 or o -1 -1 -1 -1 -1 53 -1 -1 20 50 -1 -1 .3 16 -1 49 -1. -1 28 14 -1 -1 -1 oo -1 -1 -1 -1 -1 5e 23 -1 -1 15 54 -1 -1 5 -1 18 49 -1 -1 13 -1 -1 -1 oo -1 -1 -1 55 -1 -1 S8 -1 9 -1 26 57 -1 41 -1. 31 -1 21 -1 -1 -1 -1 -1 oo -1 -1 -1 10 49 -1 59 -1 1 -1 -1 JO -1 18 -1 48 -1 7 59 -1 -1 -1 -1 oo -1 48 -1 -1 50 le -1 -1 11 52 -1 59 -1. -1 37 -1 10 or -1 -1 -1 -1 -1 oo -1 24 16 -1 -1 or 53 -1 -1 41 -1 38 51 -1 58 -1 59 8 -1 -1 -1 -1 -1 or

In another implementation it is possible to use the following compact matrix "1 to obtain 6480 bit code words with an encoding rate of 2/3:

78 -1 -1 167 237 -1 3 -1 266 -1 -1 1 n02 153 -1 -1 212 -1 or -1 -1 -1 -1 -1 -1 -1 83 189 -1 -1 68 - 1 178 -1 90 205 -1. -1 13 4 -1 -1 oo -1 -1 -1 -1 -1 -1 226 147 -1 46 -1 -1 76 -1 116 -1 211 -1 112 -} 118 -} -1 oo -} -} -} -} 92 -1 -1 214 -1 236 241 -1} 57 -1 143 -1 214 -1 207 -1. -} -1 -} or o -} -} -}

144 -1 -1 258 264 -1 53 -1 114 -1 172 -1. -1 82 262 -1 62 -1 -1 -1 oo -1 -1 -1 153 120 -1 -1} 99 -1 126 -1 61 -1 183 15 -1 -} 134 -1 -1 -} - 1 -1 oo -1 -1 100 -1 141 -1 36 -1 17 -1 156 -1 124 162 -1 -1 57 O -1 -1 -1 -1 -1 OO 196 -1 187 -1 73 - 1 80 -1 139 -1 57 -1 -1 236 267 -1 62 256 -1 -1 -1 -1 -1 O

In another implementation it is possible to use the following compact matrix "1 to obtain code words of 1152 bits with a coding rate of 5/6:

-

1 13 32 47 41 24 -1 25 22 40 1 31 8 15 20 15 42 30 13 3 -1 or -1 -1 25 46 15 43 45 29 39 47 23 38 39 12 -} 21 -} 38 33 OO -1 39 OO -} 35 45 45 38 14 16 6 11 -1 18 7 41 35 17 32 45 41 -1 le 17 or -1 oo 9 32 6 22 26 31 9 8 22 32 40 4 18 40 36 -1 -} 23 31 41 39 20 -} O

In another implementation it is possible to use the following compact matrix to obtain code words

H1

5184 bits with an encoding rate of 5/6:

-

1 47 146 203 184 112 -1 116 103 181 3 140 38 68 91 70 191 138 62 14 -1 or -1 -1 117203 67194206133114 212104171 176 56 -1% -1167149 1 -1177 oo -1 153 206 198 173 55 72 28 53 -1 82 34 186 161 eo 144 204 le7 -1 e4 77 or -1 oo

44 147 27 83 118130 41 38 100 146 183 19 85 180 163 -1 -1 106140 les 177 94 -1 or

An implementation in which the puncture technique is used starts from a code word with 1152 bits and coding rate of 5/6 and applies the following

puncture pattern

pp ~;:; IS) = [1 1 ... 1 O O ... O 1 1 ... 1 O O. •. O1

'----------- v-- ~~~ 720 36 360 36

to get a code word of 1080 bits and coding rate of 16/18.

Another implementation in which the puncture technique is used starts from a code word with 5184 bits and coding rate of 5/6 and applies the following puncture pattern

pp \\ ~ IS) = [1 1 ... 1 O O ... O 1 1 ... 1 O O ... O 1 1 ... 1 1

'-.r -----' '-.r -----' '-y -----' '-., .-' '-.r -----' 3240 162 972 162 648

to get a code word of 4860 bits and coding rate of 16/18.

Another implementation in which the puncture technique is used starts from a code word with 1152 bits and coding rate of 5/6 and applies the following puncture pattern

pp: ¡;; 21) = [1 1 ... 1 O O ... O 1 1 ... 1 O O ... O 1 1 ... 1 1

'-.r -----' '-., .-' '-v ----- "' -v -''- v ------- '720 48 240% 48

to get a code word of 1008 bits and coding rate of 20/21.

Finally, a final implementation in which the puncture technique is used starts from a code word with 5184 bits and 5/6 coding rate and applies the following puncture pattern

pp \ ¡:: 21) = [O O ... O 1 ... 1 O O ... O 1 1 ... 1 1

---------------

'------ and ------- ~~

216 43W 432 216

to get a code word of 4536 bits and coding rate of 20/21.

Next, in order to facilitate a better understanding of this descriptive report and forming an integral part thereof, some figures are attached in which the object of the invention has been represented by way of illustration and not limitation.

BRIEF DESCRIPTION OF THE FIGURES Figure 1.- Represents the block diagram of the encoder in the transmitter. Fi.gura 2. - Represents the block diagram of the decoder in the receiver. Figure 3 -Show the bipartite graph of matrix H of the example. Fi.gura 4. - Represents the flow chart of the construction of a structured LOPC code.

DESCRIPTION OF AN EXAMPLE OF EMBODIMENT OF THE INVENTION

Next, the description of an embodiment of the invention is made, referring to the numbering adopted in the figures.

The problem that the invention process wants to solve, from a theoretical point of view, is to optimize the correction of errors in data communications using low-cost hardware implementations, using LPDC codes.

An LOPC code is a linear code that operates on blocks of information. The code is defined by its parity matrix H.. In this exemplary embodiment the codes will be binary codes, but it is possible to generalize the invention to codes on any Galois field

GF (q), being q ~ 2. In transmission we will have information blocks composed of K bits. Said information block is called u ~ [u (O), II (l), ..., u (K -1)]. After applying the invention procedure a word of a linear code will be generated

v = [v (O), v (I), ..., v (N -I)] with N bits (where N> K). That code is

generates through the product v:; ::::: uG where G is a matrix

I

K xN binary generator of the LPDC code. The set of possible codes generated will be called set e and the

I

coding rate or code rate (rate) will be

R = K / N.

Therefore, it is possible to define a code E of coding rate R as the set of vectors VE e

2K

generated by all the possible binary vectors when applying the generating matrix G. An equivalent definition would be that e is the ial vector space of N dimensions covered by the compound base of the K lines of the matrix C. Another alternative way of defining the code e it is through its mat r iz of parity H, which is the form most used in the state of the art. This matrix, of dimensions (N-K) xN, has as its lines the basis of

space

dual and, Y by the so much GH T = 0 Any vector

of the

code satisfies

vH T

= 0

(being

"YOU he operator of transposition).

When using these codes from a practical point of view, it is preferable to consider the codes as systematic codes, that is, those in which the bits of the code word are among the information bits. Without losing generality this example will focus on the case when v = [u lp] 'being

p = [p (O), p (I), ..., p (N -K -1)] a vector composed of the bits of

parity, or the block of information to be transmitted and v the word code actually transmitted (after including the LPDC code).

An example of

realization

in the one who may be observed the relationship between the

matrix

from parity Y a word of the code In East

example,

he code has a rate from coding of R ::: I / 2

Y

be define through the next matrix from parity:

5

or 1

OR O o one

O o

one OR one OR one

H;

one one OR OR OR one OR

OR

OR

O o

OR

O o

OR

In this matrix, the left section corresponds to the K = 5 bits of information while the right section corresponds to the N-K = 5 bits of parity.

vH T

10 Applying the equation = 0 to the matrix H the following system of equations is obtained:

urO) + u (l) + u (3) + prO) + p (3) + p (4); O u (O) + u (1) + u (2) + prO) + p (2) + p (4); O u (O) + u (I) + u (2) + u (4) + p (I) + p (3); O u (2) + u (3) + u (4) + p (O) + p (l) + p (2); O u (3) + u (4) + p (l) + p (2) + p (3) + p (4); OR

15 An LDPC code can also be represented graphically with a bi-partite graph called Tanner-graph. In a Tanner graph the vertices are classified into two groups

or disjoint sets: the "variable vertices" (variable nodes), which represent the bits of word 20 of the code, and the "control vertices" (check nodes) that represent parity relationships. Between both sets of vertices are the possible edges that define the parity equation. In the case of the code defined in the previous example, its corresponding graph

25 is represented in Figure 3, where we will find 10 vertices of variables (14) and 5 control vertices (16),

joined by multiple edges (15). Each control vertex is linked by edges to 6 vertices of variables, as represented in the previous system of equations. It is possible to observe that the graph has as many control vertices and variables as lines and columns have the corresponding parity matrix, and that an edge will be found between the control vertex i and the

vertex of variable j when the element h (i, j) of the matrix, that is, the one located on line i ;;;;; Or, ..., N-K-1 and column j; :::: Or, ..., N -l, is nonzero.

On the other hand, it is possible to define cycles on LDPe codes, where a cycle of length 2c is defined as the path of 2c edges of length that you visit and control vertices and c vertices of variables in the Tanner graph that represents the code before returning to the same start node. To optimize the performance of the code, it is possible to demonstrate that it is of vital importance that the number of short cycles be the minimum possible. The minimum length cycle is called a loop (girth). In particular, it is desirable that the girth be greater than 4 to avoid reducing the performance of an iterative decoder.

In the original description, R. Gallager presented codes whose parity matrices were generated randomly. In the state of the art it is of general knowledge that to obtain good performance, near the Shannon limit, the code size must be relatively large and as a result the matrix of

parity

should from be from big dimensions . He trouble is

that

matrices from big dimensions Y generated

randomly

hinder the implementation so much of the

Encoder as the decoder. One way to avoid this difficulty is to use matrices with a structure

regular . To generate a regular structure, the following steps would be followed:

one . - Initially a binary model matrix is generated

HQ of dimensions (n-k) xn where n <N, k <K and R = k / n = K / N.

If the Hamming weight of the columns and lines of "o is constant, the code generated is called regular LDPC. However, it is possible to obtain better performance if the matrix is irregular, that is, if the weights of the columns follow a dependent statistical distribution of the coding rate and the channel where the data transmission is finally carried out.

2. -Once the binary model matrix "01 is obtained, the compact matrix K¡ is generated, replacing each element equal to" 1 "of" or with a positive integer O "::; x <b

(where b ~ N / n) pseudo-randomly and each element equal to "OH by the value -l.

3 . -To obtain the parity matrix H, the positive elements of are replaced by a sub-matrix

H1

i cyclically rotated dentistry and the number of times indicated by the value of the positive element in question and the

H1 elements equal to -1 are replaced by a null sub-matrix of the same dimension. The dimension of these sub-matrices will be equally bxb.

The result is a matrix of parity H of dimensions (N-K) xN that defines an LOPC code of coding rate R = K / N. The degree of density Isparseness) of the matrix will depend on the magnitude b. Generally, how much

greater b better performance is obtained using an iterative decoder.

If the generated matrix cycles (Tanner graph)

5 turn out to be very short, step 2 (or even step 1 if necessary) is repeated in order to improve these properties.

To facilitate the implementation of the encoder 10, it is necessary to generate the binary model matrix "or in a specific way. First, this matrix is divided into two

H - [H IH J H.

o-b parts where the submatrix corresponds to the

to

H

positions of the information bits and the parity bits. The first submatch is generated pseudo15 randomly in the manner described below. However, the second section is usually deterministic. H

This second section according to the state of the art, and to be able to design an efficient encoder will take one of the following two forms: the first form is

hb (ü)

O ü hb (1)

1 o

or

hb (n -k-l)

O o

where the first section is a pseudo-column vector

Random weight Hammi ng greater than 2 and a double and diagonal matrix whose elements os hbl (i, j) are equal to "1" when

and equal to "O" in the rest of the 25 positions.

.

H

The second way to generate is totally double diagonal

or

or

one

OR

OR

OR

OR

where the submatrix elements hb (i, j) are equal to i = j i = j + 1

5 "1" when, and equal to "O" in the rest of the positions. Once this base matrix structure is generated, the matrix

Compact is generated in the manner described above with the sole exception that in the double diagonal part H,

10 of, "1" are replaced by the same positive integer and \\ 0 "by" -1 ". Similarly, the final parity matrix is obtained by changing the positive integers for cyclically rotated identities and the negative integers for a null submatrix. The procedure can be observed

15 graphically in Figure 4, where block (17) generates the Ho

binary model matrix block (18) generates matrix H,

Compact the block (19) decides if the cycles are long enough, so that the matrix of parity H is generated with the block (20), or if the 20 cycles are short, the model matrix is generated again (21 )

or the base matrix (22) is regenerated.

The method and device of invention

25 modifies the structure of the parity matrix known in the state of the art to facilitate the final implementation of coding and decoding and improve the

ES 2 386449 Al

benefits . For this, the proposed structure consists of

that

the section from the matrix model binary

correspondent

to the bits from parity have the next

shape :

h ,, (O)

o o

1 o

h ,, (l)

OR

h ,, (n-k -l)

OR

where the structure H bl is triple diagonal, that is also

of the elements of the two central diagonals hb1 (i, O I

hb1 U + 1, i), the diagonal element of the last line

hb1 (n-k-J, O) is also equal to "1". The compact matrix is

10 generates in the manner described above unless the last line element equal to "1n is replaced by a strictly positive integer w2: O.

A binari model matrix a "o for r = 1/2 with n = 24 and k = 12 could have the following structure:

15 or 00 or 00000 0000000000 000 000 o o 000000000

o 0000 o o 00 00000000 0000 o o 00 00 0000000 o o 0000000000 000000

20 or 000000 or 00000 o o o o o 00 o 00000000000 o o o o o o 0000000000000 o o o

o 000000 00000000 o o o o o o o o o o 000000000 o

25 0000 0000 000000000 00000000 000000000

A compact matrix "1 derived from the previous one for a block size N = 336 and therefore with an expansion factor b = 14 would be the following:

13 -1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1

S -1 -1 -1 11 -1 -1 -1 4 -1 6 -1 or o -1 -1 -1 -1 -1 -1 -1 -1 -1

ES 2 386449 Al

2 o

-

1 1.3 -1 -1 -1 -1 11 -1 10 -1 9 13 -1 -1 OO -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 13 -1 -1 6 - 1 10 -1 S -1 -1 -1 -1 OO -1 -1 -1 -1 -1 -1 -1 -1 -1 8 8 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1

, "

-

1 .3 -1 -1 -1 -1 -1 -1, -,, -1 -1 -1 -1 -, OO -1 -1 -1 -1 -1 -1 -1 -, 9 -1 - 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 -1 -1

-

1 13 -1 9 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 -1 -1 11 -1 -1 -1 -1 - 1 -1, 11 12 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 -1 -1 -1 10 -1 -1 -1 -1 -1 13 13 -1 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 -1 or -1 -1 or -1 -1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 -1 -1 -1 -1 -1 -1 12 -1 -1 -1 -1 -1 -1 -1 -1 -1 W

"

or preferably, the following matrix can be used as an alternative:

-

} -} -} -} -1 9 6 -} -1 -1 -1 or -1 -} -1 -} -1 -} -} -} -} -}

-

, or -1 -1 -1 .3 -1 12 -1 -1 .3 -} oo -1 -1 -1 -1 -1 -1 -1 -1 -} -1 9 11 -1 -1 13 - 1 -1 12 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1

-1 -1 11 -1 -1 -1 -1 -1 11 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 8 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 3 or -1 -1 8 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 or 6 -1 -1 -1 -1 5 13 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 9 -1 -1 -1 3 -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1

9 or 13 -1 -1 12 -1 -1 8 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 5 -1 -1 -1 - 1 5 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 8 -1 -1 8 -1 -1 9 or -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 OO 10 11 -1 -1 -1 3 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 - 1 -1 -1 -1 O

For a different block size we can define a different compact matrix that can be derived from the same binary model matrix or from a different one.

To obtain code words of 1920 bits with an encoding rate of 1/2 you can use the matrix:

-

1 52 -1 64 -1 -1 60 -1 -1 -1 -1 1 -1 O -} -1 -} -1 -} -1 -} -1 -} -1

10 -1 -1 -1 -1 "-1 -1 79 -1 78 51. -1 or O -1 -1 -, -, -1 -1 -, -, -, 9 -1 -1 -1 - 1 -1 -1 75 29 72 -1 -1 -, O or -1 -, -, -1 -1 -, -, -,

-

1 52 16 63 -1 -1 65 -1 -1 -1 -1 -1 40 -1 -1 or O -1 -1 -1 -1 -1 -1 -1 -1 24 -1 -1 47 39 - 1 -1 -1 -1 -1 -} -1 -} -1 OO -} -1 -1 -1 -} -1 52 -1 -1 -1 -1 -1 -1 -1 53 "48 -1 -} -1 -} -1 -} OO -1 -1 -1 -} -1 -1 O -1 -1 72 -1 67 57 -1 -1 -1 -1 -} -1 -} -1 - 1 -1 OO -1 -1 -} -1 -1 7 -1 -1 -1 50 -1 -1 -1 -1 15 -} -1 -1 -1 -} -1 -} OO -1 -1 -1 15 -1 19 -1 -1 -1 -1 -1 75 51 43 -1 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 72 -1 -1 -1 38 -1 -1 -1 69 -1 62 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 19 -1 41 -1 -1 41 -1 -1 -1 -1 O -1 -} -1 -1 -1 -} -1 -} -1 OO 41 -1 17 -1 -1 -1 -1 -1 1S -1 JO -1 40 6 -1 -1 -1 -1 -1 -1 -1 -1 -1 or

or, preferably, the matrix:

27 -1 -} -1 55 19 -} M -1 -1 -} -1 -1 O -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 O -1 -1 70 -1 47 -1 ~ -1 -1 OO -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 41 -1 -1 -1 44 -1 -1 59 W 25 -1 -1 O or -1 -1 -1 -1 -1 -1 -1 -1 16 n -1 -1 -1 -} 48 -1 -1 -} -1 -1 -1 -1 or O -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 45 -1 27 -1 46 19 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 - 1 -1 -1 -1 -1 63 -1 -1 -1 55 -1 -1 -1 48 26 10 -1 -1 -1 -1 OO -1 -1 -1 -1 -1

ES 2 386449 Al

-1 -1 -1 42 -1 21 -1 SS -1 41 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 -1 -1 -1 -1 -1 -1 78 O -1 7 52 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1 -1 -1 29 9 -1 -1 -1 37 -1 -1 -1 35 21 -1 -1 -1 -1 -1 -1 -1 -, O or -1 -1 -1 -1 22 72 -1 -1 47 -1 -1 -1 O -1 -1 -1 -1 - 1 -1 -1 -1 -1 -1 OO -1 35 -1 -1 -1 -1 13 -1 35 -1 70 -1 -1 O -1 -1 -1 -1 -1 -1 -1 - 1 -1 OO -1 46 28 -1 -1 -1 31 -1 -1 -1 e -1 10 58 -1 -1 -1 -1 -1 -1 -1 -1 -1 or

A compact matrix for bits with an e xpansion 360 factor derived from a different binary model matrix would be the following:

-

} -1 -} -1 -} -1 297 106 328 -1 -} 99 -1 or -1 -} -1 -} -1 -} -1 -} -1 -} 290 or 312 -1 32 -1 120 -1 -1 -1 -1 -1 -} oo -} -1 -1 -1 -1 -1 -1 -1 -1

18.3 57 -1 -1 187 68 -1 -1 -1 -1260 -1 81 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 323 -1 -1 - 1 137 354 -1 -1 162 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 -1228 -1 -1 -1 -1224 -1 114 -1245 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 113 98 -1 -1 120 23 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 138 -1 187 45 62 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 - 1 -1 142 -1 -1 -1 347 67 -1 -1 -1 46 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 328 265 -1 66 156 96 -1 - 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 212 184 -1 -1 102 -1 -1 -1 -1 120 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 60 15 -1 329 153 or -1 -1 -1 -1 -1 -1 -1 -1 -1 oo 207 70 -1 1 235 -1 -1 -1 -1 -1 -1 -1 81 185 -1 -1 -1 -1 -1 -1 -1 -1 - 1st

Another preferred alternative to obtain code words of 8640 bits with a coding rate of 1/2 is the matrix:

-

1 34 -1 95 -1 279 -1 -1 -1 -1 248 -1. -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 or -1 -1 -1 -1 134 356 275 -1 oo -1 -1 - 1 -1 -1 -1 -1 -1 -1 51 -1 27 -1 -1 -1 -1 -1 22 152 -1 57 -1 -1 oo -1 -1 -1 -1 -1 -1 - 1 -1 -1 124 -1 290 -1 281 15 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 340 -1 99 336 -1 -1 1 -1 -1 -1 -1 33 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 163 -1 46 -1 -1 -1 -1 -1 -1 306 -1 86 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 185 -1 24 -1 -1 -1 94 or -1 -1 -1 -1 -1 - 1 -1 -1 -1 oo -1 -1 -1 -1 -1 223 -1 225 325 -1 -1 -1 -1 -1 297 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 46 -1 314 -1 -1 -1 59 -1 -1 67 -1 120 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 - 1 121 -1 -1 -1 -1 161 -1 303 -1 264 -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 303 -1 8 -1 185 -1 - 1 138 -1 -1 -1. o -1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 312 -1 -1 -1 100 -1 -1 144 -1 307 33 166 -1 -1 -1 -1 -1 -1 -1 -1 -1 O

The step from compact matrix to binary model is univocal but the opposite step is not, that is, from a binary model matrix we can obtain different compact matrices. The binary matrix is introduced as a step that facilitates the description of the invention. It is possible to develop a compact matrix directly without going through the model matrix

binary In this case, from said compact matrix it is possible to obtain its corresponding binary model matrix which, if it is triple diagonal, will be in accordance with the method of the invention.

Error correction codes can be "punctured" ~ where the puncturing technique involves removing elements of the code word so that they are not transmitted. Instead of transmitting a code word v = [veO), v (l), ..., veN -1)] a

word w = [IY {O), w (l), ..., IY {M -1)], where M <N. The puncture must be done in a controlled manner, so that the necessary redundancy is transmitted so that the receiver decoder is able to estimate the transmitted information. This puncture applies to both the information bits and the parity bits. It is possible to define a puncture pattern as the sequence of bits to be transmitted as punctures, where said bit pattern can be periodic or aperiodic. In the case of not having any regularity, said pattern can be described with a PP vector of N positions, indicating in it with a "l H the bits to be transmitted and with" OH the bits to be eliminated (punctured) . Thanks to the puncture technique it is possible to increase the communication of information, since less is being sent

redundancy

Yes he weight Hamming of the Pattern PP is M the

rate

total of the system from coding from mistakes is

R = K / M

For example, if we have a code with R = 5/6 and block size N = 5 l84 and we want to perform a puncture to increase the rate to R = 16 / l8 we can use the following puncture pattern so we will obtain a block with N = 4860 bits:

pp \ ',%' "~ [1 1 ... 1 O O ... O 1 ... 1 O O ... O 1 1 ...

'-v-' '-v ------' '-v-' '---- v-' '----- v-'

3240 162 972 162 648

An electronic device is used to implement the LOpe code encoder, either a program run on a microprocessor or a hardware implementation in FPGA or ASIC. Said device receives an information block, calculates the parity bits, concatenates them next to the information bits and delivers them to the next stage of the transmitter to be properly modulated and transmitted by the corresponding channel. The calculation of parity bits can

be through the product with the generating matrix G or through the solution of the system of equations presented above.

The LDPe code decoder is usually based on an iterative decoder. A possible decoder, among several options of the state of the art, consists of an estimator that upon receiving the word corresponding to the

r = v + z

code transmitted being Z additive noise of the

channel, estimates z noise so that

(r-z) H '~ O

In the event that the system makes use of the puncture technique, before the decoder there will be a unit that inserts an indicator in the punctured positions. This indicator is used for the decoder to estimate the appropriate value in these positions.

Figure 1 shows the block diagram of a typical encoder, where (1) is the block of information to be transmitted u = [u (O), u (I), ..., u (K ~ 1)] , (2) is a

memory containing the representation of the matrix of IJarity H or of the generating matrix G, (3) is said matrix,

(4)

is the block that performs the coding algorithm,

(5)

is the linear code word obtained from the coding v = [v (O), v (I) "", v (N -I)], (6) is the block that performs the puncturing technique and (7 ) is the word obtained after the puncture w = [w (O), w (1) ,,,,, w (M -1)].

5 Figure 2 shows the block diagram for a decoder, where (8) represents the signal received from the

channel S "" [so, s¡, ..., S, lf_I J I that will be similar to the word obtained after the puncture but after being affected by the noise of the channel, (9) represents the block that performs the function of

10 "punctured", obtaining a word (10) r = [r (O), r (I) ,,,., R (N-I)] with the number of bits of the LPDC code.

(11) is the memory that contains either the parity matrix

or the generator matrix in the receiver, and transmits it

(12) to the block that performs the decoder algorithm (13). 15 The output of this block will be the recomposed information

(14) íi = [ü (O), ü (l), ..., ü (K -1)].

Claims (15)

one . Data communication procedure through 5 noisy media, which is applied in the encoding of data in transmission and that generates parity bits on a block of information so that from a word of K bits a code word of N bits is generated; characterized in that it comprises the steps of: 10 -select a factor b consisting of a natural number l ~ b ~ K so that N / b = n and K / b = k are natural numbers;

-

generate a binary model matrix Ho = [HaI Hbl of size (nk) xn as the combination of a submatrix corresponding to the positions of the information bits Ha and a submatrix corresponding to the parity bits Hb, where said second submatrix Hb [h bO IHblJ is composed of a column vector of nk positions hbO and a triple diagonal Hbl structure, where the elements of the two central diagonals hbl (i, i), hhl (i + l, i), O ~ i ~ nk-2 and of the

20 diagonal of the last row hb1 (n-k -l, O) are equal to 1, where n-k is the number of rows and columns of the Hb matrix, and the rest of the elements are equal to zero; generate a compact matrix H1 from the binary model matrix Ho. 25 -generate the parity matrix H from the compact matrix Hl;

-

select a block of information;

dfJllcdL Id lIldLL "L :: de pdL" lddd H oübLe the information blüque to determine the parity bits 30 corresponding to said block; Y ES 2 386449 Al transmit the parity bits together with the information block. 2 . Data communication procedure through 5 noisy media according to claim 1 characterized in that the following compact matrix Hl is used to obtain 336-bit code words with a coding rate of 1/2: -1 -1 -1 6 -1 -1 6 -1 -1 2 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 10 -1 or -1 -1 -1 3 -1 12 1 -1 -1 3-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 9 11 -1 -1 13 -1 -1 2 12 -1 - 1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 11 -1 -1 7 -1 -1 -1 11 -1 -1 -1 -1 or - 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 to -1 -1 -1 -1 -1 4-1-1-1 or -1 -1 -1 -1 -1 -1 ., or -1 -1 8 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 15 -1 -1 -1 6 -1 - 1 -1 -1 5 13 -1 -1 -1 -1 -1 -1 -1 0-1-1-1-1 -1 -1 -1 9 -1 -1 -1 3 -1 -1 1 - 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 o 13 -1 -1 12 -1 -1 6 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 -1 -1 5 -1 -1 4 -1 - 1 5 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 o., -1 -1 -1 8 -1 -1 8 -1 -1 or -1 or - 1 -1 -1 -1 -1 -1 -1 -1 -1 or 20 10 11 -1 -1 -1 3 -1 -1 O -1 -1 -1 8 -1 -1 -1 -1 -1 -1 -1 -1 -1 3 . Procedure for communicating data through noisy means according to claim 1 characterized in that the following compact matrix H1 is used to obtain code words 1920 bits with a coding rate of 1/2: 27 -1 -1 -1 55 19 -1 30 -1 -1 -1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 1 -1 70 -1 47 -1 62 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 41 -1 -1 -1 44 -1 -1 59 60 25 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 30 16 77 -1 -1 -1 5 -1 48 -1 -1 -1 -1 -1 -1 -1 o -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 45 -1 27 -1 46 19 -1 -1 -1 -1 -1 -1 -1 O -1 -1 -1 -1 -1 -1 -1 -1 63 -1 -1 -1 55 -1 -1 -1 48 26 10 -1 -1 -1 -1 O -1 -1 -1 -1 -1 -1 -1 -1 42 -1 21 -1 58 -1 41 -1 -1 -1 -1 -1 -1 -1 -1 0-1-1-1-1 -1 -1 -1 -1 78 O -1 7 52 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0-1-1-1 35 -1 29 9 -1 -1 -1 37 -1 -1 -1 35 21 -1 -1 -1 -1 -1 -1 -1 -1 O -1 -1 -1 -1 22 72 -1 -1 47 -1 -1 -1 O -1 -1 -1 -1 -1 -1 - 1 -1 -1 -1 0-1 35 -1 -1 -1 -1 13 -1 35 -1 70 -1 -1 O -1 -1 -1 -1 -1 -1 -1 -1 -1 - 1 46 2B -1 -1 -1 3B -1 -1 -1 8 -1 10 58 -1 -1 -1 -1 -1 -1 -1 -1 -1 or 40 4. Data communication procedure through noisy means according to claim 1 characterized in that the following compact matrix is used at 8 1 for ES 2 386449 Al get c6di go words of 8640 bits with a coding rate of 1/2:

-

1 34 -1 9 $ -1 219 -1 -1 -1 -1 248 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 () - 1 or -1 -1 -1 -1 134 356 215 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 5 51 -1 27 -1 -1 -1 -1 -1 22 152 -1 57 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 -1 124 -1 290 -1 281 15 -1 -1 -1 -1 -1 -1 -1 - 1 or -1 -1 -1 -1 -1 -L -1 -1 340 -1 99 336 -1 -1 1 -1 -1 -1 -1 33 -1 -1 -1 or -1 -1 -1 -1 -1 -1 163 -1 46 -1 -1 -1 -1 -1 -1 306 -1 86 -1 -1 -1 -1 -1 or -1 -1 -1 -1 -1 -1 185 -1 24 -1 -1 -1 94 or -1 -1 -1 -1 -1 -1 -1 -1 -1 0-1-1-L-1

10 -1 223 -1 225 325 -1 -1 -1 -1 -1 297 -1 -1 -1 -1 -1 -1 -1 -1 or -1 -1 -1 46 -1 314 -1 -1 -1 59 -1 -1 67 -1 120 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 121 -1 -1 -1 -1 161 -1 303 - 1 264 -1 -1 -1 -1 -1 -1 -1 -1 -1 0-1 -1 303 -1 8 -1 195 -1 -1 138 -1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 -1 312 -1 -1 -1 100 -1 -1 144 -1 307 33 166 -1 -1 -1 -1 -1 -1 -1 - eleven 5 . Device for communication of data through noisy media, which is applied in the encoding of data in transmission, characterized in that the encoder comprises:

-

means for storing a compact matrix 81 derived from

20 a binary model matrix Ho [Ha I Hb] formed as the combination of a submatrix corresponding to the positions of the information bits Ha and a submatrix corresponding to the parity bits Hb, where said second submatrix H b = [hb O IH bi] is made up of a vector 25 column of nk positions h bO and a structure H bl triple diagonal, where the elements of the two central diagonals hb1 (i, i), hb1 (i + l, i), O ~ i ~ nk-2 and of the diagonal of the last row hb dn-k-1, O) are equal to 1, where nk is the number of rows and columns of the Hb matrix, and the rest 30 elements are equal to zero;

-

a microprocessor comprising means for selecting an information block, applying the compact matrix to generate the parity matrix H, applying the parity matrix H to the information block to obtain the parity bits corresponding to said block and affixing the bits

ES 2 386449 Al of parity to the block of information before it is transmitted. 6. Device for communicating data through noisy means according to claim 5, characterized in that the following compact matrix is used to obtain code words of 336 bits with a coding rate of 1/2: -1 -1 -1 6 -1 -1 6 -1 -1 2 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 -1 - 1 3 -1 12 1 -1 -1 3-1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 9 11 -1 -1 13 -1 -1 2 12 -1 - 1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 11 -1 -1 7 -1 -1 -1 11 -1 -1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 to -1 -1 -1 -1 -1 4-1-1-1 or -1 -1 -1 -1 -1 -1 -, -1 -1 to -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 6 -1 -1 -1 -1 5 13 -1 -1 -1 -1 -1 -1 -1 0- 1-1-1-1 -1 -1 -1 -1 -1 -1 3 -1 -1 3 1 -1 -1 -1 -1 -1 -1 -1 0-1-1-1 o 13 -1 -1 12 -1 -1 a -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 -1 -) 5 -1 -1 4 -1 - 1 5 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -, -1 -1 -1 e -1 -1 e -1 -1 or -1 or - 1 -1 -1 -1 -1 -1 -1 -1 -1 or 10 11 -1 -1 -1 3 -) -1 or -1 -1 -1 8 -1 -1 -1 -1 -1 - 1 -1 -) -1

7. Data communication device through noisy means according to claim 5, characterized in that the following compact matrix is used to obtain code words 1920 bits with a coding rate of 1/2:

8. Data communication device through noisy means according to claim 5 characterized in that the following compact matrix is used to obtain

27

-one -one -one 55 19 -one 30 -one -one -one -one -one or -one -one -one -one -one -one -one -one -one -one

-one

-one

or  -one one  -one 70  -one 47  -one 62  -one  -one or

-one

-one

-one

-one

-one

-one

-one

-one

-one

_one

_one

41  _one  _one  _one 44  _one  _one _ ~ q 60 n  _one  _one or or

_one

_one

_one

_one

_one

_one

_one

_one

16

77 -one -one -one 5 -one 49 -one -one -one -one -one -one -one OR -one -) -one -one -one -one -one

-one

-one

-one

Four. Five  -one 27  -one 46 19  -one  -one  -one  -one  -one  -one  -one or -)

-one

-one

-one

-one

-one

-)

-one 63  -) -one -one 55 -one -one  -) 48 26 ) 0 -one -one  -) -one or -one -one  -) -one -one

-one

-one

-one

42  -one twenty-one  -one H.H  -one 4l  -one  -one  -one  -one  -one  -one  -one  -one or -1-1-1-1

-one

-one

-one

-one

78 or  -one 7 52  -one  -one  -one  -one  -one  -one  -one  -one  -one  -one 0-1-1-1

-one

29 9  -one  -one  -one 37  -one  -one  -one 35 twenty-one  -one  -one  -one  -one  -one  -one  -one  -one or -1

-one

-one

-one

22 72  -one  -one 47  -one  -one  -one OR  -one  -one  -one  -one  -one  -one  -one  -one  -one  -one or -,

35

-one -one -one -one 13 -one  35 -one 70 -one -one OR -one -one -one -one -one -one -one -one -one OR

-one

46 28  -one  -one  -one 39  -one  -one  -one 9  -one 10 59

-one

-one

-one

-one

-one

-one

-one

-one

-one

8640 bit code words with an encoding rate ES 2 386449 Al

-

1 34 -1 95 -1 279 -1 -1 -1 -1 249 -1 -1 O -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 O -1 O -1 -1 -1 -1 134 356 275 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 51 -1 27 -1 -1 -1 -1 -1 n 152 -1 57 -1 -1 O -1 -1 -1 -1 -1 -1 -1 -1 -1 124 -1 290 -1 ZSI 15 -1 -1 -1 -1 -1 -1 -1 -1 or - 1 -1 -1 -1 -1 -1 -1 5 -1 340 -1 99 336 -1 -1 1 -1 -1 -1 -1 33 -1 -1 -1 or -1 -1 -1 -1 -1 -1 163 -1 46 -1 -1 -1 -1 -1 -1 306 -1 86 -1 -1 -1 -1 -1 O -1 -1 -1 -1 -1 -1 195 -1 24 -1 -1 -1 94 O -1 -1 -1 -1 -1 -1 -1 -1 -1 0-1-1-1-1 -1 223 -1 225 325 -1 -1 -1 - 1 -1 297 -1 -1 -1 -1 -1 -1 -1 -1 O -1 -1 -1 46 -1 314 -1 -1 -1 59 -1 -1 67 -1 120 -1 -1 -1 -1 -1 -1 -1 -1 OO -1 -1

10 -1 -1 121 -1 -1 -1 -1 161 -1 303 -1 264 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -, -1 303 -1 e -1 lBS -1 -1 138 -1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 -1 312 -1 -1 -1 100 -1 -1 144 - 1 307 33 166 -1 -1 -1 -1 -1 -1 -1 -1 -1 9. Data communication procedure through 15 noisy means, which is applied in the decoding of data in reception and that estimates the block of information from a received signal vector, so that a word of K bits is obtained from a received code word of N bits; characterized in that it comprises the steps of: 20 -select a channel signal vector; calculate a binary model matrix Ho = [H IHbJ as the combination of a submatrix corresponding to the positions of the information bits Ha and of a submatrix corresponding to the parity bits Hb, where said Second submatrix Hb = [hbO IHb1] is composed of a column vector of n-k positions hbO and a structure Hbl. triple diagonal, where the elements of the two central diagonals hb1 (i, i), hb1 (i + l, i), O ~ i ~ nk-2 and the diagonal of the last row hb¡ (nk -l, O) are equal to 1, being nk 30 the number of rows and columns of the Hb matrix, and the rest of the elements are equal to zero; generate a compact matrix H1 from the binary model matrix Ho; generate the parity matrix H from the compact matrix 35 H1; Y ES 2 386449 Al estimate the block of information from the received signal vector and the parity matrix H. 10. Data communication procedure through 5 noisy media according to claim 9 characterized in that the following compact matrix H1 is used to obtain 336-bit code words with a coding rate of 1/2: -1 -1 -1 6 -1 -1 6 -1 -1 2 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 10 -1 or -1 -1 -1 3 -1 12 1 -1 -1 3-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 9 11 -1 -1 13 -1 -1 2 12 -1 - 1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 11 -1 -1 7 -1 -1 -1 11 -1 -1 -1 -1 or - 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 to -1 -1 -1 -1 -1 4-1-1-1 or -1 -1 -1 -1 -1 -1 -, or -1 -1 8 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 15 -1 -1 -1 6 -1 - 1 -1 -1 5 13 -1 -1 -1 -1 -1 -1 -1 0-1-1-1-1 -1 -1 -1 9 -1 -1 -1 3 -1 -1 1 - 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 o 13 -1 -1 12 -1 -1 6 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 -1 -1 5 -1 -1 4 -1 - 1 5 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -, -1 -1 -1 8 -1 -1 8 -1 -1 or -1 or - 1 -1 -1 -1 -1 -1 -1 -1 -1 or 20 10 11 -1 -1 -1 3 -1 -1 O -1 -1 -1 8 -1 -1 -1 -1 -1 -1 -1 -1 -1 eleven . Procedure for communicating data through noisy media according to claim 9 characterized in that the following compact matrix Hl is used for 25 get 1920 bit code words with a coding rate of 1/2: 27 -1 -1 -1 55 19 -1 JO -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 1 -1 10 -1 41 -1 62 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 4l -1 -1 -1 44 -1 -1 59 60 25 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 30 16 77 -1 -1 -1 S -1 48 -1 -1 -1 -1 -1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 45 -1 n -1 46 19 -1 -1 -1 -1 -1 -1 -1 O -1 -1 -1 - 1 -1 -1 -1 -1 6J -1 -1 -1 55 -1 -1 -1 48 26 10 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 42 -1 21 -1 S8 -1 41 -1 -1 -1 -1 -1 -1 -1 -1 0-1-1-1-1 -1 -1 -1 -1 18 O -1 1 52 - 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 35 -1 29 9 -1 -1 -1 37 -1 -1 -1 35 21 -1 -1 - 1 -1 -1 -1 -1 -1 or -1 -1 -1 -1 22 72 -1 -1 47 -1 -1 -1 O -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0-1 35 -1 -1 -1 -1 13 -1 35 -1 70 -1 -1 O -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 46 28 -1 -1 -1 38 -1 -1 -1 8 -1 10 58 -1 -1 -1 -1 -1 -1 -1 -1 -1 40 12. Method of communicating data through noisy means according to claim 9 characterized because the following compact matrix H1 is used to ES 2 386449 Al get c6di go words of 8640 bits with a coding rate of 1/2:

-

1 34 -1 9 $ -1 219 -1 -1 -1 -1 248 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 () - 1 or -1 -1 -1 -1 134 356 215 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 5 51 -1 27 -1 -1 -1 -1 -1 22 152 -1 57 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 -1 124 -1 290 -1 281 15 -1 -1 -1 -1 -1 -1 -1 - 1 or -1 -1 -1 -1 -1 -L -1 -1 340 -1 99 336 -1 -1 1 -1 -1 -1 -1 33 -1 -1 -1 or -1 -1 -1 -1 -1 -1 163 -1 46 -1 -1 -1 -1 -1 -1 306 -1 86 -1 -1 -1 -1 -1 or -1 -1 -1 -1 -1 -1 185 -1 24 -1 -1 -1 94 or -1 -1 -1 -1 -1 -1 -1 -1 -1 0-1-1-L-1

10 -1 223 -1 225 325 -1 -1 -1 -1 -1 297 -1 -1 -1 -1 -1 -1 -1 -1 or -1 -1 -1 46 -1 314 -1 -1 -1 59 -1 -1 67 -1 120 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 121 -1 -1 -1 -1 161 -1 303 - 1 264 -1 -1 -1 -1 -1 -1 -1 -1 -1 0-1 -1 303 -1 8 -1 195 -1 -1 138 -1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 -1 312 -1 -1 -1 100 -1 -1 144 -1 307 33 166 -1 -1 -1 -1 -1 -1 -1 - eleven 13. Data communication device through noisy media, which is applied in the decoding of data at reception; characterized in that the decoder comprises:

-

means for storing a compact matrix Hl derived from

20 a binary model matrix Ho [Ha I Hb] formed as the combination of a submatrix corresponding to the positions of the information bits Ha and of a submatrix corresponding to the Hb parity bits, where said second submatrix Hb [hbO IHbd is composed of a vector 25 column of nk hbO positions and a triple diagonal Hbl structure, where the elements of the two central diagonals hb1 (i, i), hb1 (i + l, i), O ::::: i ::::: nk-2 and the diagonal of the last row hbdn-k -1, O) are equal to 1, nk being the number of rows and columns of the Hb matrix, and the rest 30 elements are equal to zero;

-

a microprocessor comprising means for generating the parity matrix H from the compact matrix Hl, applying said parity matrix H on the received signal vector, and estimating the block of information received.

ES 2 386449 Al 14. Data communication device through noisy means according to claim 13, characterized in that the following compact matrix is used to obtain code words of 336 bits with a coding rate of 1/2: -1 -1 -1 6 -1 -1 6 -1 -1 2 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 -1 - 1 3 -1 12 1 -1 -1 3-1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 9 11 -1 -1 13 -1 -1 2 12 -1 - 1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 11 -1 -1 7 -1 -1 -1 11 -1 -1 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 to -1 -1 -1 -1 -1 ~ -1-1-1 or -1 -1 -1 -1 -1 -1 ~, -1 -1 8 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 oo -1 -1 -1 -1 -1 -1 -1 -1 6 -1 -1 -1 -1!> 13 -1 -1 -1 -1 -1 -1 -1 0-1-1-1-1 -1 -1 -1 9 -1 -1 -1 3 -1 -1 3 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 o 13 -1 -1 12 -1 -1 8 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1.-1 -1 5 -1 -1 4 -1 -1 5 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ~, -1 -1 -1 9 -1 -1 9 -1 -1 or -1 or - 1 -1 -1 -1 -1 -1 -1 -1 -1 • 10 11 -1 -1 -1 3 -1 -1 or -1 -1 -1 e -1 -1 -1 -1 -1 -1 -1 -1 -1 or fifteen . Data communication device through noisy means according to claim 13 characterized in that the following compact matrix is used to obtain 1920 bit code words with a coding rate of 1/2:

27

-one -one -one 55 19 -one 30 -one -one -one -one -one or -one -one -one -one -one -one -one -one -one -one

-one

-one

or  -one one  -one 70  -one 47  -one 62  -one  -one or

-one

-one

-one

-one

-one

-one

-one

-one

-one

-one

-one

41  -one  -one  -one 44  -one  -one 59 60 2S  -one  -one or

-one

-one

-one

-one

-one

-one

-one

-one

16

77 -one -one -one 5 -one 48 -one -one -one -one -one -one -one or -one -one -one -one -one -one -one

-one

-one

-one

Four. Five  -one 27  -one 46 19  -one  -one  -one  -one  -one  -one  -one or

-one

-one

-one

-one

-one

-one

-one

-one

63  -one  -one  -one 55  -one  -one  -one 48 26 10  -one  -one  -one  -one OR

-one

-one

-one

-one

-one

-one

-one

-one

42  -one twenty-one  -one be  -one 4l  -one  -one  -one  -one  -one  -one  -one  -one 0-1-1-1-1

-one

-one

-one

-one

78 OR  -one 7 52  -one  -one  -one  -one  -one  -one  -one  -one  -one  -one 0-1-1-1

-one

29 9  -one  -one  -one 37  -one  -one  -one 35 twenty-one  -one  -one  -one  -one  -one  -one  -one  -one OR

-one

-one

-one

-one

22 72  -one  -one 47  -one  -one  -one or  -one  -one  -one  -one  -one  -one  -one  -one  -one  -one 0

-one

35

-one -one -one -one 13 -one  35 -one 70 -one -one or -one -one -one -one -one -one -one -one -one or

-one

46 28  -one  -one  -one 38  -one  -one  -one 8  -one 10 58

-one

-one

-one

-one

-one

-one

-one

-one

-one

16. Device for communicating data through noisy means according to claim 13, characterized in that the following compact matrix is used to obtain code words of 8640 bits with a coding rate of 1/2:

-

1 34 -1 95 -1 279 -1 -1 -1 -1 248 -1 -1 or -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 or -1 or -1 -1 -1 -1 134 356 275 -1 or -1 -1 -1 -1 -1 -1 -1 -L -1 51 -1 27 -1 -1 -1 -1 -1 n 152 -1 57 -1 -1 O -1 -1 -1 -1 -1 -1 -1 -1

ES 2 386449 Al

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-

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-

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5

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10

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